冀教版（2024）新教材八年级数学上册第十二章12.2.2 分式的除法 同步练习.docx

12.2　分式的乘除课时2　分式的除法知识点1 分式的除法1.化简(-1x)÷1x2的结果是 (　　)A.-x B.x C.-1x D.1x2.化简a2-1a2+2a+1÷a-1a的结果是 (　　)A.12 B.aa+1 C.a+1a D.a+1a+23.若3-2xx2-4÷(　　)=1x+2,则(　　)中的式子为 (　　)A.3-2xx+2 B.3-2xx-2 C.2x-3 D.x-23-2x 4.若a+b=5,则代数式 b2-a2a÷a-b2a 的值为 (　　)A.-10 B.10 C.-25 D.-525.如果(a3b2)2÷(ab3)2=3,那么a8b4等于 (　　)A.6 B.9 C.12 D.816.计算:a-ba+b÷(b-a)=　　　　.7.七年级二班教室后墙上的“学习园地”是一个长方形,它的面积为6a2-9ab+3aab,相邻两边中一边长为3ab,则另一边长为　　　　.8.计算:(1)8y2x÷2xy2;(2)x2-9x2+6x+9÷x-3x+3;(3)x2-8x+164-x2÷16-x24+4x+x2.9.先化简,再求值:aa2-2a+1÷1a-1,其中a=3.10.已知ba=12,求a2-b2a2-2ab+b2÷ab+b2a2-ab的值.知识点2 分式的乘除混合运算11.计算a÷ab×ba的结果是 (　　)A.a　 B.b2a　 C.a2　 D.1a212.计算:(x2-9)·xx-3÷1x=　　　　.13.已知a2-a=10,则a-1a+2·a2-4a2-2a+1÷1a2-1的值为　　　　.14.计算:(1)x2-xyx2+xy·(x+y)÷xy-y2xy;(2)a2-81a2+6a+9÷9-a2a+6·a+3a+9.参考答案1.A　【解析】　(-1x)÷1x2=-1x×x2=-x.故选A.2.B　【解析】　a2-1a2+2a+1÷a-1a=(a-1)(a+1)(a+1)2×aa-1=aa+1.故选B.3.B　【解析】　∵3-2xx2-4÷1x+2=3-2x(x-2)(x+2)·(x+2)=3-2xx-2,∴(　　)中的式子为3-2xx-2.故选B.4.A　【解析】　b2-a2a÷a-b2a=(b-a)(b+a)a·2aa-b=-2(a+b)=-2×5=-10.故选A.5.B　【解析】　∵(a3b2)2÷(ab3)2=3,∴a6b4×b6a2=3,∴a4b2=3,∴a8b4=(a4b2)2=9.故选B.6. -1a+b　【解析】　a-ba+b÷(b-a)= a-ba+b·1-(a-b)=-1a+b.7. 2a-3b+1a　【解析】　∵长方形的面积是6a2-9ab+3aab,相邻两边中一边长为3ab,∴它的另一边长为6a2-9ab+3aab÷3ab=2a-3b+1a.8.【解析】　(1)8y2x÷2xy2=8y2x·12xy2=4x2.(2)x2-9x2+6x+9÷x-3x+3=(x+3)(x-3)(x+3)2·x+3x-3=1.(3)x2-8x+164-x2÷16-x24+4x+x2=(x-4)2-(x+2)(x-2)·(x+2)2-(x+4)(x-4)=(x-4)(x+2)(x-2)(x+4).9.【解析】　aa2-2a+1÷1a-1=a(a-1)2·(a-1)=aa-1,当a=3时,原式=33-1=32.10.【解析】　a2-b2a2-2ab+b2÷ab+b2a2-ab=a2-b2a2-2ab+b2·a2-abab+b2=(a+b)(a-b)(a-b)2·a(a-b)b(a+b)=ab.因为ba=12,所以原式=2.11.B　【解析】　a÷ab×ba=a×ba×ba=b2a.故选B.12. x2(x+3)　【解析】　(x2-9)·xx-3÷1x=(x+3)(x-3)·xx-3·x=x2(x+3).13.8　【解析】　a-1a+2·a2-4a2-2a+1÷1a2-1=a-1a+2·(a-2)(a+2)(a-1)2·(a+1)(a-1)=(a+1)(a-2)=a2-a-2,∵a2-a=10,∴原式=10-2=8.14.【解析】　(1)x2-xyx2+xy·(x+y)÷xy-y2xy=x(x-y)x(x+y)·(x+y)·xyy(x-y)=x.(2)a2-81a2+6a+9÷9-a2a+6·a+3a+9=a2-81a2+6a+9·2a+69-a·a+3a+9=(a+9)(a-9)(a+3)2·[-2(a+3)a-9]·a+3a+9=-2.。